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Knot Invariants from Representations of Braids by Automorphisms of a Free Group 用自由群的自同构表示辫的结不变量
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-09-22 DOI: 10.1007/s10469-025-09800-6
V. E. Shpilrain
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引用次数: 0
Sessions of the Seminar “Algebra i Logika” “代数与逻辑学”研讨会分会场
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-09-18 DOI: 10.1007/s10469-025-09801-5
{"title":"Sessions of the Seminar “Algebra i Logika”","authors":"","doi":"10.1007/s10469-025-09801-5","DOIUrl":"10.1007/s10469-025-09801-5","url":null,"abstract":"","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 5","pages":"395 - 398"},"PeriodicalIF":0.6,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145256773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Number of Countable Models of a Complete Theory and of Its Inessential Extension 完备理论的可数模型数及其非本质推广
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-09-05 DOI: 10.1007/s10469-025-09789-y
K. Zh. Kudaibergenov
{"title":"The Number of Countable Models of a Complete Theory and of Its Inessential Extension","authors":"K. Zh. Kudaibergenov","doi":"10.1007/s10469-025-09789-y","DOIUrl":"10.1007/s10469-025-09789-y","url":null,"abstract":"<p>It is proved that (<i>a</i>) there exists a complete countable theory having 2<sup><i>ω</i></sup> countable models, some inessential extension of which has <i>ω</i> countable models, and that (<i>b</i>) there exists a complete countable theory having 2<sup><i>ω</i></sup> countable models, some inessential extension of which has finitely many countable models. This gives an answer to the question of A. D. Taimanov.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 4","pages":"258 - 269"},"PeriodicalIF":0.6,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Letter to the Editorial Board 给编委会的信
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-09-02 DOI: 10.1007/s10469-025-09793-2
M. V. Schwidefsky
{"title":"Letter to the Editorial Board","authors":"M. V. Schwidefsky","doi":"10.1007/s10469-025-09793-2","DOIUrl":"10.1007/s10469-025-09793-2","url":null,"abstract":"<p>This short note contains necessary addenda and corrections to [1].</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 4","pages":"294 - 299"},"PeriodicalIF":0.6,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A New Version of Orthogonality for 1-Types in Weakly o-Minimal Theories 弱o-极小理论中1型正交性的一个新版本
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-09-01 DOI: 10.1007/s10469-025-09791-4
B. Sh. Kulpeshov, S. V. Sudoplatov
{"title":"A New Version of Orthogonality for 1-Types in Weakly o-Minimal Theories","authors":"B. Sh. Kulpeshov,&nbsp;S. V. Sudoplatov","doi":"10.1007/s10469-025-09791-4","DOIUrl":"10.1007/s10469-025-09791-4","url":null,"abstract":"<p>We introduce a new version of orthogonality for nonalgebraic 1-types in weakly o-minimal theories, that of almost quite orthogonality. It is stated that the non almost quite orthogonality relation is an equivalence relation. The main result is a criterion for a weakly o-minimal theory of finite convexity rank with 1 &lt; I(T, ω) &lt; 2<sup>ω</sup> to have exactly 3<sup>m</sup>6<sup>l</sup> countable pairwise nonisomorphic models for some nonnegative integers m, l &lt; ω in terms of the orthogonality version presented.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 4","pages":"270 - 283"},"PeriodicalIF":0.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sessions of the Seminar “Algebra i Logika” “代数与逻辑学”研讨会分会场
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-08-30 DOI: 10.1007/s10469-025-09794-1
{"title":"Sessions of the Seminar “Algebra i Logika”","authors":"","doi":"10.1007/s10469-025-09794-1","DOIUrl":"10.1007/s10469-025-09794-1","url":null,"abstract":"","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 4","pages":"300 - 303"},"PeriodicalIF":0.6,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
CEA-Operators and the Ershov Hierarchy. II cea -算子和Ershov层次。2
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-08-28 DOI: 10.1007/s10469-025-09788-z
M. M. Arslanov, I. I. Batyrshin, M. M. Yamaleev
{"title":"CEA-Operators and the Ershov Hierarchy. II","authors":"M. M. Arslanov,&nbsp;I. I. Batyrshin,&nbsp;M. M. Yamaleev","doi":"10.1007/s10469-025-09788-z","DOIUrl":"10.1007/s10469-025-09788-z","url":null,"abstract":"<p>We continue and finalize our research started in [Algebra and Logic, <b>63</b>, No. 3 (2024), 168–178]. It is proved that there exists a noncomputable low c.e. set <i>A</i> such that any set that is <i>CEA</i>(<i>A</i>) and 2-c.e. has a c.e. degree.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 4","pages":"235 - 248"},"PeriodicalIF":0.6,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Gelfand–Kirillov Conjecture as a First-Order Formula 一阶公式的Gelfand-Kirillov猜想
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-08-26 DOI: 10.1007/s10469-025-09792-3
H. L. Mariano, J. Schwarz
{"title":"The Gelfand–Kirillov Conjecture as a First-Order Formula","authors":"H. L. Mariano,&nbsp;J. Schwarz","doi":"10.1007/s10469-025-09792-3","DOIUrl":"10.1007/s10469-025-09792-3","url":null,"abstract":"<p>We show that for a given (reduced) root system Σ and for any algebraically closed field k with zero characteristic, the validity of the Gelfand–Kirillov conjecture for the finite-dimensional Lie algebra <span>({mathfrak{g}}_{mathrm{k},Sigma },)</span> the sole semisimple Lie algebra over k with root system Σ, is equivalent to the provability of a certain first-order sentence in the language of rings <span>(mathcal{L})</span>(0, 1, +, ∗, −) in the theory ACF<sub>0</sub> of algebraically closed fields of zero characteristic.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 4","pages":"284 - 293"},"PeriodicalIF":0.6,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalized Baumslag–Solitar Groups Universally Equivalent to Tree Groups 广义baumslag -孤子群普遍等价于树群
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-08-26 DOI: 10.1007/s10469-025-09790-5
F. A. Dudkin
{"title":"Generalized Baumslag–Solitar Groups Universally Equivalent to Tree Groups","authors":"F. A. Dudkin","doi":"10.1007/s10469-025-09790-5","DOIUrl":"10.1007/s10469-025-09790-5","url":null,"abstract":"<p>A finitely generated group that acts on a tree so that all vertex and edge stabilizers are infinite cyclic groups is called a generalized Baumslag–Solitar group (<i>GBS</i> group). Every <i>GBS</i> group is the fundamental group <i>π</i><sub>1</sub>(𝔸) of a suitable labeled graph 𝔸. If 𝔸 is a labeled tree, then we call <i>π</i><sub>1</sub>(𝔸) a tree GBS group. It is known that <i>GBS</i> groups isomorphic to tree groups are themselves tree groups. It is shown that <i>GBS</i> groups universally equivalent to tree groups do not have to be tree groups. Moreover, we give a description of all <i>GBS</i> groups that are universally equivalent to tree groups.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 4","pages":"249 - 257"},"PeriodicalIF":0.6,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Locally Finite Groups Containing Direct Products of Dihedral Groups 含二面体群的直积的局部有限群
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-05-14 DOI: 10.1007/s10469-025-09785-2
A. A. Shlepkin
{"title":"Locally Finite Groups Containing Direct Products of Dihedral Groups","authors":"A. A. Shlepkin","doi":"10.1007/s10469-025-09785-2","DOIUrl":"10.1007/s10469-025-09785-2","url":null,"abstract":"<p>We prove the theorem stating the following. Let <i>G</i> be a locally finite group saturated with groups from a set 𝔐 consisting of direct products of <i>d</i> dihedral groups. Then <i>G</i> is a direct product of d groups of the form <i>B</i> ⋋ &lt;υ&gt;, where <i>B</i> is a locally cyclic group inverted by an involution υ.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 3","pages":"217 - 227"},"PeriodicalIF":0.4,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144091051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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